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310                              CHEMICAL ENGINEERING
Bottom discharge is often the most convenient way of disposing of the solids particularly if they will slide through freely like coffee, small castings, etc.
The accompanying chart (p. 308) shows the centrifugal force which will be obtained with baskets of varying diameter and with the ordinary ranges of revolution.
The Sharpies Centrifuge.In this machine the bowl revolves from 20,000 to 40,000 r.p.m. and an effect is secured in separating solids, emulsions and matter in the colloidal state which is out of the range of the ordinary centrifugal separator. The formula for centrifugal force as given in the textbooks is F equals Wtf/gr. If for t;2 is substituted its equivalent 4ir2r*N2 and replacing the radius r by the diameter D, F becomes equal to 2Wv*DN*/g. Increasing the number of revolutions, N, increases the centrifugal force very much faster than increasing the diameter of the bowl as the centrifugal force increases as the square of the number of revolutions and only directly as the diameter. As in boiler problems the pressure tending to burst the bowl is equal to the centrifugal force expressed in pounds per square inch times the area of the section passing through the center of the bowl divided by two. If the internal diameter of the bowl is 30 in. and its depth 20 in. the area of the section on which the bursting pressure is figured will be 600 sq. in. It is evident then that other things being equal that high centrifugal force can be most readily obtained by bowls of small diameter revolving at high speed and it is the application of these two principles which is employed in the Sharpies centrifuge.
Figure 31 shows a section of the separator for making liquid separations there being two discharge spouts as the figure will show. These machines are rotated by a steam turbine. The means of suspension, resistance to shock and of enabling the bowl and contents to maintain the position of its center of gravity constant in position will be evident from the diagram. See p. 321 for detailed list of parts.
The size of the machines range from a bowl diameter of 1% in. and with a depth of 9 in. which is a laboratory machine to a factory size with bowl diameter 4% in. and a length of 36 in.
Some of the commercial uses which the machine suggests are the recovery of oil from soap stock, the dehydration of crude petroleum and emulsions, the separation of amorphous wax from cylinder stock and the recovery of wool grease from waste scouring liquors. A brief description of the last application will make the commercial use of the machine plain.
The figures are based on handling 30,000 Ib. of wool a day with an average shrinkage of 60 per cent and using 4 Ib. of water per pound of wool. As much as 14 Ib. of water to the pound of wool are used in scouring but with centrifuging in view the amount used should be as small as possible and with less water there is a great saving in soap effected. Each No. 6 Sharpies will handle 120 gal. of scouring liquor per hour and for 120,000 gal. of liquid 14 machines will be required and one dehydrating centrifuge for the grease from the primary machines for a 10-hr, day. These 15 machines will cost $15,000 and with extra parts the cost will run to $16,000. The manufacturers estimate the cost for power for the centrifuges will be about 2 cts. per hour per machine and that the yearly cost of operating the centrifugal plant will be about $10,000 including interest on the investment and depreciation.
The greasy liquors from the scouring bowls are first run to settling tanks so as to settle out sand and dirt and are kept at a temperature of 160F. They are then run by gravity to the primary centrifuges from which grease containing 30 per cent moisture can be discharged. From the centrifuges the watery grease is removed and dumped into a grease tank which is equipped with steam coil and agitator. To the recovered